Question: Simplify the following expression: $ n = \dfrac{-7}{2} + \dfrac{-4p - 9}{-3p} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-3p}{-3p}$ $ \dfrac{-7}{2} \times \dfrac{-3p}{-3p} = \dfrac{21p}{-6p} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{-4p - 9}{-3p} \times \dfrac{2}{2} = \dfrac{-8p - 18}{-6p} $ Therefore $ n = \dfrac{21p}{-6p} + \dfrac{-8p - 18}{-6p} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{21p - 8p - 18}{-6p} $ $n = \dfrac{13p - 18}{-6p}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{-13p + 18}{6p}$